Depending on types of molded products, it sometimes is desirable to more sharply increase the injection speed at the beginning of an injection process. To this end, in conventional hydraulic injection molding machines an accumulator is connected to a hydraulic injection cylinder for supplying pressurized operating oil at a large flow rate to the cylinder. On the other hand, electrically-operated injection molding machines employ injection servomotors capable of producing a large output with small inertia. However, injection molding machines equipped with accumulators or injection motors capable of large output with small inertia are costly.